I think the suit looks really good and only needs minor alterations (other than the sleeves, I would definitely order it with fake buttons to avoid this). I would get it remade because of the sleeves, unless you can find a tailor that can shorten them.
How is the quality of the suit? How would you say it compares to something like Hugo Boss. Is the chest slightly big because you measured yourself incorrectly or just the way they cut it and is that the slim fit?

Hopefully the one you bought is cut differently. The one I tried had 34 in pants! I considered trying a 36 but the sleeves are an inch longer than the 38 short and on the 38 i had to remove about as much as you could get away with without having to shorten at the shoulder. I'm 5'6, 31 in waist, 38in chest.

Why is that? Do short people in Europe tend to be fat or something? It's just strang that the starting short size would run so big. Anyways, its too bad because I love their suits but because of the working buttonholes, buying a regular size would be impossiple for me.